NEW YORK (CBSNewYork) – Cardinal Timothy Dolan is continuing to speak out against the Obama administration’s controversial birth control mandate a day after Catholic institutions around the country filed a lawsuit against the policy.

Speaking on “CBS This Morning” Tuesday, Dolan said the “federal government seems to be radically intruding into the internal definition on what the church is.”

The policy requires most employers to provide birth control coverage as part of their employee health plans and was adopted by Health and Human Services in an effort to improve health care for woman.

The original policy was for religiously affiliated non-profits, including hospitals, colleges and charities, but allowed churches and other houses of worship to opt out.

But after the rule caused a furor with Catholic groups, President Obama softened the policy so that insurers would pay for birth control instead of religious groups, but Dolan said that isn’t enough.

“First of all, it’s doesn’t help us too much because most Catholic entities are self-insured so we’re still going to be paying for it anyway,” Dolan said. “But secondly, it still gives no attention to these choking mandates, to this choking definition of religion.”

According to Dolan, in order to be exempt from the mandate and considered a church, the institution can only serve and employ Catholics, a definition he called “strangling.”

“When did the government get into the business of defining for us the extent of our ministry,” he said. “If they would just simply mitigate the strangling nature of those definitions for exemptions, we would be able to say at least we’ll be able to preserve our ministries and services.”

The lawsuits filed Monday are the biggest push against the mandate since it was announced by Obama in January.

But while Dolan said Tuesday that the debate is “about religious freedom” and “not about contraception,” not everyone agrees.

In a statement on its website, Planned Parenthood said Monday that access to birth control is a “critical health and economic concern for American women.”

“It is unbelievable that in the year 2012 we have to fight for access to birth control,” Cecile Richards, president of Planned Parenthood Federation of America, said in the statement. “This isn’t a religious or political issue – it’s a medical issue, and that’s where we should keep it.”

More than 40 Catholic organizations are included in the lawsuits against the Obama administration.